AQA A-Level Physics: Use of SI Units and Their Prefixes — Practice Questions

These are original questions written for Marlbridge, in the style and at the standard of the examination. They are not reproduced past-paper questions — examination boards hold copyright in their own papers. Use these alongside the official past papers available free from your board.

Related: Use of SI Units and Their Prefixes study guide

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Section A

1. State the six fundamental (base) quantities named in the specification, with their SI units. [6]

2. State which SI base quantity is deliberately excluded from this specification’s list of fundamental quantities. [1]

Section B

3. Explain the difference between a base unit and a derived unit, giving one example of each. [3]

4. Show, using base units, that the newton (N) is equivalent to kg m s⁻². [2]

5. A student writes a length as “45 cm” in a calculation that also uses SI base units. Explain why this is a problem, and state what the student should do instead. [2]

6. Convert 2.5 × 10⁻¹⁵ J into electronvolts, given 1 eV = 1.6 × 10⁻¹⁹ J. [2]

7. A domestic energy meter records 4.2 kW h of electrical energy used. Convert this to joules, given 1 kW h = 3.6 × 10⁶ J. [2]

8. Express 6.8 × 10⁻⁹ m using an appropriate SI prefix rather than standard form. [2]

9. A student writes a current as “250 mA” but then substitutes 250 directly into an equation that requires SI base units. Explain the error and give the corrected value in amperes. [2]

10. A resistor has a value quoted as “4.7 MΩ”. State this resistance in base SI units (ohms), in standard form. [2]

11. A student is asked to name the fundamental (base) SI unit of mass, and answers “the newton”. Explain why this is incorrect, and give the correct answer. [2]

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Answers

1. Mass — kilogram (kg) [1]; length — metre (m) [1]; time — second (s) [1]; amount of substance — mole (mol) [1]; temperature — kelvin (K) [1]; electric current — ampere (A) [1].

2. Luminous intensity (the candela) is excluded from the specification [1].

3. A base unit is one of the seven fundamental units SI is built from (this specification examines six, excluding luminous intensity) and is not defined in terms of any other unit, e.g. the kilogram [1] [1]. A derived unit is built by combining base units according to the physical relationship that defines the quantity, e.g. the newton, derived from mass × acceleration [1].

4. Force = mass × acceleration [1]. Acceleration has units m s⁻², so force has units kg × m s⁻² = kg m s⁻² [1], which is exactly what one newton means in base units.

5. Mixing a non-SI-base unit such as centimetres into a calculation that otherwise uses SI base units (metres) will make the answer wrong by a power of ten [1]. The student should convert 45 cm to 0.45 m before substituting it into the equation [1].

6. eV = J ÷ (1.6 × 10⁻¹⁹) [1]. eV = 2.5 × 10⁻¹⁵ ÷ 1.6 × 10⁻¹⁹ = 1.5625 × 10⁴ eV (≈ 1.6 × 10⁴ eV) [1].

7. J = kW h × 3.6 × 10⁶ [1]. J = 4.2 × 3.6 × 10⁶ = 1.512 × 10⁷ J [1].

8. 6.8 × 10⁻⁹ m corresponds to the prefix nano (10⁻⁹) [1], so the value is written as 6.8 nm [1].

9. The student has substituted the number 250 as if it were in amperes, when “mA” means the value is actually in milliamps, a factor of 10³ smaller than an ampere [1]. The corrected value is 250 × 10⁻³ = 0.25 A [1].

10. M is the prefix mega, meaning ×10⁶ [1], so 4.7 MΩ = 4.7 × 10⁶ Ω [1].

11. The newton is the unit of force (weight), not mass – it is a derived unit, built from mass × acceleration, not one of the six fundamental quantities [1]. The correct fundamental unit of mass is the kilogram (kg) [1].

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Where marks are usually lost

• Confusing prefixes with similar-sounding names or nearby exponents — for example milli (10⁻³) with micro (10⁻⁶), or mega (10⁶) with giga (10⁹).
• Substituting a value directly into an equation without first converting it into SI base units, especially with lengths given in cm or mm, or currents given in mA.
• Reporting a converted answer without adjusting its significant figures or standard-form power to match the size of the new unit.
• Naming mass (kg) when a question asks for a fundamental quantity’s unit but actually means weight (a force, measured in N).
• Forgetting that the specification’s excluded quantity is luminous intensity (candela), not one of the six fundamental quantities students must know.

Approaching SI units and prefixes questions

The two AQA-specified unit conversions – joules to electronvolts, and joules to kilowatt-hours – both work the same way: identify which direction the conversion factor multiplies or divides, then check the answer’s order of magnitude makes sense for the physical situation described (a tiny particle energy should come out as a small number of eV once divided by 1.6 × 10⁻¹⁹, not a huge one). The same discipline applies to prefix questions: convert the given value into full standard form first, then match the exponent to the nearest prefix in the table, rather than trying to jump straight from one prefix to another. Treat every calculation question as an SI-base-units check first – if any quantity is still in a prefixed or non-base unit, converting it before substituting is what most consistently separates a fully correct answer from one that is wrong by a clean power of ten.